We investigate the excitation of the propagating scalar degree of freedom—the scalaron—in quadratic f(R) gravity by localized Maxwell-Higgs vortices in a \((2+1)\) -dimensional BTZ black hole spacetime. In the perturbative regime where the higher-curvature coupling is small compared to the AdS scale, the modified trace equation reduces to a massive Klein-Gordon equation for the Ricci scalar, sourced by the vortex energy-momentum tensor. Using the Sturm-Liouville structure of the radial operator, we construct the exact radial Green function and obtain the curvature profile for an arbitrary localized source. Outside the vortex core, the induced curvature perturbation exhibits a universal power-law decay \(R(r) \sim r^{-(1+\nu )}\) , independent of the microscopic vortex structure, where the exponent \(\nu \) coincides with the standard AdS mass-dimension relation. We demonstrate that the scalar excitation is linearly stable, satisfies the Breitenlohner-Freedman bound, carries finite total energy, and produces exponentially suppressed backreaction on the BTZ geometry, ensuring the smooth recovery of the Einstein limit. These results provide an analytically tractable realization of how higher-curvature corrections activate local gravitational dynamics in three dimensions.
